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Diffstat (limited to 'langfassung/docs')
| -rw-r--r-- | langfassung/docs/2_einleitung.tex | 47 | ||||
| -rw-r--r-- | langfassung/docs/3_hauptteil.tex | 49 | ||||
| -rw-r--r-- | langfassung/docs/4_ergebnisse.tex | 26 |
3 files changed, 120 insertions, 2 deletions
diff --git a/langfassung/docs/2_einleitung.tex b/langfassung/docs/2_einleitung.tex index 806c214..bce9ec8 100644 --- a/langfassung/docs/2_einleitung.tex +++ b/langfassung/docs/2_einleitung.tex @@ -1,3 +1,4 @@ +op Einleitung \subsection{Themen} @@ -16,4 +17,50 @@ Einleitung \subsection{Motivation} +\paragraph{ \( \Phi \) } + +\begin{equation} + \Phi(r) = - \frac{4\pi G \rho_0 R_s^3}{r} \ln ( 1+ \frac{r}{R_s} ) +\end{equation} + +with the limits + +\begin{equation} + \lim_{r\to \infty} \Phi=0 +\end{equation} + +and + +\begin{equation} + \lim_{r\to 0} \Phi=-4\pi G\rho_0 R_s^2 +\end{equation} + +\paragraph{ \( \rho \) } + +\begin{equation} + \rho(r) = \frac{1}{\sqrt{2 \cdot \pi} \cdot \sigma} \cdot + e^{\left( - \frac{(\Phi(r)}{\sigma^{2}} \right)} +\end{equation} + +\paragraph{\( \rho_{new} \rightarrow (deriviation) \) } + +\begin{equation} + \rho(r) \cdot 1-\frac{1}{(2 \cdot sigma^{2} )} \cdot + ( Mxx \cdot x^{2} + 2 \cdot Mxy \cdot xy + Myy \cdot y^{2} )) +\end{equation} + +% def rho_new(x, y, z): +% a = (1 - ((1) / (2 * (sigma ** 2))) * ( Mxx * x**2 + 2 * Mxy * x * y + Myy * y**2 ) ) +% return rho(x, y, z) * a +% +% # phi function +% def phi(x): +% if x == 0: +% return -4 * pi * f_0 * G * R_s**2 +% +% a = - ( 4 * pi * G * f_0 * R_s ** 3 ) / x +% b = np.log(1. + (x / R_s) ) +% c = a * b +% return c + Motivations blah diff --git a/langfassung/docs/3_hauptteil.tex b/langfassung/docs/3_hauptteil.tex index eab3897..5174f08 100644 --- a/langfassung/docs/3_hauptteil.tex +++ b/langfassung/docs/3_hauptteil.tex @@ -43,14 +43,59 @@ Blender is Awesome, Python is Awesome and together they are \subsection{Making things faster} -Kicking out to many Stars, 1 out of 10000 is just to much... +\paragraph{ Kicking out to many Stars, 1 out of 10000 is just to much... } +~\\ + +\begin{itemize} + \item Use a custom Density function for each Axis + \begin{itemize} + \item \( \phi(r_x)\), \( \phi(r_y) \) and \( \phi(r_z) \) + \item more controll + \end{itemize} +\end{itemize} + +\begin{tikzpicture} +\begin{scope} + + \node[draw] (H) at (0,-2) + {\( \phi(x_1) > rand_x \)}; + \node[draw] (I) at (5,-2) + {\( \phi(y_1) > rand_y \)}; + \node[draw] (J) at (10,-2) + {\( \phi(z_1) > rand_z \)}; + + \node[draw] (K) at (10, -4) {true}; + \node[draw] (L) at (0, -4) {false}; + + \node[draw] (M) at (10, -6) {write data to data.csv}; + + \node[draw] (N) at (0, -6) {generate new random coordinates}; + +\end{scope} + +\begin{scope} [every node/.style={fill=white,circle}, + every edge/.style={draw=red,very thick}] + + \path[->] (H) edge (K); + \path[->] (I) edge (K); + \path[->] (J) edge (K); + \path[->] (H) edge (L); + \path[->] (I) edge (L); + \path[->] (J) edge (L); + + \path[->] (K) edge (M); + \path[->] (L) edge (N); + +\end{scope} + +\end{tikzpicture} \subsection{Spiral Galaxies} The previous Galaxy models where all using a completely spherical model, generating a spiral galaxy is just not possible using these models. -\subsubsection{N-Körper problem} +\subsubsection{N-body problem} Kurze Beschreibung des N-Körper Problems diff --git a/langfassung/docs/4_ergebnisse.tex b/langfassung/docs/4_ergebnisse.tex index abd806d..088b13e 100644 --- a/langfassung/docs/4_ergebnisse.tex +++ b/langfassung/docs/4_ergebnisse.tex @@ -22,6 +22,32 @@ Pro MegaByte können die Koordinaten von 10000 Sternen gespeichert werden. Die generierung von Spiralgalaxien gestaltet sich schweiriger als erwartet. +\subsection{Lookup-Table Speed} + +\begin{tabular}{l | l | l} +rho-values & step & time (in seconds) \\ \hline\hline +1500000 & 1 & 8.07 \\ +750000 & 2 & 4.4 \\ +375000 & 4 & 2.26 \\ +187500 & 8 & 1.35 \\ +93750 & 16 & 0.76 \\ +\end{tabular} + +The correlation between the number of stars generated and the time needed ist +clearly linear. + +\paragraph{Python script} ~\\ +\lstset{language=Python} +\begin{lstlisting}[frame = single] +import matplotlib.pyplot as plt + +list_time = [8.07, 4.4, 2.26, 1.35, 0.76] +list_rho_values = [1500000, 750000, 375000, 187500, 93750] + +plt.plot(list_time, list_rho_values, '-ro') +plt.show() +\end{lstlisting} + \subsection{Distortion of Galaxies} Galaxien verformen dinge |
